Stochastic locality and master-field simulations of very large lattices

TL;DR

This paper discusses master-field simulation techniques in lattice QCD, demonstrating their potential for large lattice computations by leveraging weak correlations in distant regions, with initial successful results in SU(3) gauge theory.

Contribution

It introduces the concept of stochastic locality and master-field simulations for large lattices, addressing key conceptual and technical challenges, and reports encouraging initial results.

Findings

Successful initial simulations of SU(3) gauge theory using master-field approach

Demonstration of weak correlations enabling single-field estimations

Potential for simulating very large lattices efficiently

Abstract

In lattice QCD and other field theories with a mass gap, the field variables in distant regions of a physically large lattice are only weakly correlated. Accurate stochastic estimates of the expectation values of local observables may therefore be obtained from a single representative field. Such master-field simulations potentially allow very large lattices to be simulated, but require various conceptual and technical issues to be addressed. In this talk, an introduction to the subject is provided and some encouraging results of master-field simulations of the SU(3) gauge theory are reported.